Multiplicity scaling in ideal and viscous hydrodynamics

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Using numerical results from ideal and viscous relativistic hydrodynamic simulations with three different equations of state, for Au+Au and Cu+Cu collisions at different centralities and initial energy densities, we explore the dependence of the eccentricity-scaled elliptic flow, v_2/epsilon, and the produced entropy fraction, Delta S/S_0, on the final charged hadron multiplicity density dN_ch/dy per unit transverse overlap area S, (1/S)(dN_ch/dy).

• The viscous hydrodynamic simulations are performed with two different versions of the Israel-Stewart kinetic evolution equations, and in each case we investigate the dependence of the physical observables on the kinetic relaxation time.
• We find approximate scaling of v_2/epsilon and Delta S/S_0 with (1/S)(dN_ch/dy), with scaling functions that depend on the EOS and, in particular, on the value of the specific shear viscosity eta/s.
• Small scaling violations are seen even in ideal hydrodynamics, caused by a breaking of the scale invariance of ideal fluid dynamics by the freeze-out condition.